Question

# Find the number of $$5$$-digit odd numbers that can be formed using the integers from $$3$$ to $$9$$ if no digit is to occur more than once in any number

A
1440
B
180
C
360
D
720

Solution

## The correct option is A $$1440$$The digits from which we can choose digits is $$3,4,5,6,7,8,9$$, that is a total of $$7$$ digits Since each desired number has to be odd , so we must have any of  $$3,5,7,9$$ at the units place. This can be done in $$4$$ ways Then  ten thousands, thousands, hundreds, and tens  place can be filled up by remaining $$6$$ digits in $$^6P_4 = \dfrac {6! }{ (6-4)! } =\quad \dfrac { 6! }{ 2! } =\quad 6\times 5 \times 4 \times 3 =\quad 360$$ waysSo, total number of $$5$$  digit odd numbers that can be formed $$= 360 \times 4 = 1440$$ Maths

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